The shape of objects cannot only be recognized by vision, but also by touch. Vision has the advantage that shapes can be seen at a distance, but touch has the advantage that during exploration many additional object properties become available, such as temperature (Jones, 2009), texture (Bensmaia, 2009), and weight (Jones, 1986). Moreover, also the invisible backside of the objects can provide shape information (Newell et al., 2001). In active touch, both the cutaneous sense (input from skin receptors) and the kinesthetic sense (input from receptors located in muscles, tendons, and joints) play a role. For such active tactual perception, the term “haptic perception” is used (Loomis and Lederman, 1986). Typical exploratory movements to determine shape by touch are “enclosure” for global shape and size, and “contour following” for exact shape (Lederman and Klatzky, 1987; Klatzky and Reed, 2009). By means of touch, both three-dimensional and two-dimensional shapes can be recognized, although the latter is much harder.

Three-dimensional shape from touch

Humans are well able to recognize familiar objects by means of touch (Klatzky et al., 1985). In an extensive study, blindfolded students were asked to haptically identify as fast as possible objects such as a comb, a carrot, a tennis racket, a padlock, a knife, and many other daily life objects. Most objects were identified correctly (96%) and were recognized within 3 s. Thus, this study established that human performance with such objects is fast and accurate. Although these authors were the first to investigate response times and accuracy in great detail, a similar test was already in use for clinical studies of sensory function (e.g., Wynn Parry and Salter, 1976).

Other studies investigating shape from touch used better-defined stimuli than just objects from daily life. Gibson (1963) asked an artist to create a set of stimuli that were “equally different” from one another, were about hand-sized, were smooth and had a regular convex backside. He concluded that his participants were able to distinguish such objects by just haptic exploration. The same stimuli were used by Norman and colleagues (2012). They showed that visual and haptic shape discrimination performance is similar as long as manipulation of the stimuli was similar to that in daily life.

Roland and Mortensen (1987) were the first who used a set of parametrically defined stimuli, such as spheres, ellipsoids and rectangular blocks of different sizes. By keeping the surface properties and the weights constant (the spheres were hollow), shape and size were the only factors distinguishing the stimuli. They were interested in the way the objects were manipulated during a size or shape discrimination task and in discrimination performance. They described a model that could predict human performance in the size discrimination task, but the results for shape discrimination were not so good. Kappers and colleagues (1994) created a set a doubly curved surfaces such as convex and concave elliptic and hyperbolic paraboloids by means of a computer-controlled milling machine. They found that hyperbolic stimuli were somewhat harder to identify than elliptic stimuli. Moreover, if the curvature of the stimuli was more pronounced, identification performance improved.

More recently, Norman et al. (2004) made plastic copies of 12 bell peppers in order to have a set of “natural” stimuli. They compared discrimination and matching performance in several conditions: using just touch, using just vision, and using both touch and vision. Performance in all conditions was very similar, which led them to conclude that the 3D representations of shape in vision and in touch are functionally overlapping. Also Gaissert and Wallraven (2012) used natural stimuli, namely a set of seashells. They compared the visual and haptic perceptual spaces and found that these are nearly identical. They suggest that haptic and visual similarity perception are linked by the same cognitive processes.

Curvature from touch

Figure 1: Illustration of how the gradient of a curved stimulus is defined as the ratio between its height h and half the stimulus length l.

An important and often investigated aspect of shape is curvature, as many smooth objects contain curved parts. Gordon and Morrison (1982) were interested in how well humans can distinguish flat from curved stimuli using active touch. Using small curved stimuli of just a few centimeters, they showed that the threshold for curvature is determined by the overall gradient of the stimulus. This gradient is the ratio between the base-to-peak height of the stimulus and half the stimulus length (see Figure 1). Goodwin and colleagues (1991) did similar experiments using passive touch, as they wanted to limit the role of sensory and motor afferents. They found that a difference in curvature of about 10% could be distinguished. In a sequel to this study (Goodwin and Wheat, 1992), the contact area between the finger and the curved stimulus was kept constant. As the thresholds remained the same, they could conclude that contact area could not be the determining factor in curvature discrimination. As larger contact areas led to smaller thresholds, their finding was consistent with that of Gordon and Morrison (1982) for active touch.

Pont et al. (1997) did similar experiments with hand-sized stimuli (and much less curved stimuli) and they also came to a similar conclusion: the difference in local slopes between two stimuli of the same length determines curvature discrimination performance. They went a step further in proving this conclusion, by creating two new sets of stimuli that either contained only height differences (so no slope and no curvature information) or contained both height and slope differences (but no curvature information) (Pont et al., 1999). Stimuli with only height information were much harder to discriminate than those with also slope and curvature information, but the sets with or without curvature indeed led to similar thresholds as long as slope information was present. Wijntjes and colleagues (2009) used a device so that similar experiments could be run in active instead of passive touch and also their experiments showed that slope information was the determining factor for curvature discrimination. An overview of many of the curvature discrimination experiments can be found in Kappers (2011).

Influence of curvature on shape from touch

Figure 2: Hand positioned on a curved surface. As the hand is longer than wide, the perceived curvature along the hand will be larger than across the hand.

Haptic curvature discrimination gets better if the length of the stimuli is larger (Pont et al., 1999). In addition, the same study showed that perception of the curvature of a stimulus is influenced by its length: if the curvature is the same, the longer of two stimuli will be perceived as more curved. This led to an intriguing prediction: as the hands are usually longer than wide, a spherical object should be perceived as an ellipsoid if judged by placing the hand on it (see Figure 2). An experiment with blindfolded participants confirmed that this is indeed the case (Pont et al., 1998).

Figure 3: Cross-sections of a cylindrical object (left) and a rectangular block (right). Illustration of the difference in aspect ratio needed for correct discrimination from circular (1.03 in the case of cylinders) and square (1.11 in the case of the rectangular blocks).

Van der Horst and Kappers (2008) performed an experiment in which participants had to distinguish cylinders with circular cross-section from those with an elliptical cross-section. In addition, they did a similar experiment with rectangular blocks, in which a square cross-section had to be distinguished from a rectangular one. In both experiments, the aspect ratio (the ratio between the longer and the shorter axes) was varied systematically. Whereas the task was the same, performance with the cylinders was much better than with the blocks: an aspect ratio of 1.03 was sufficient for the cylinders, whereas 1.11 was necessary for the rectangular blocks (see Figure 3). They concluded that the curvature information in the cylindrical stimuli aided in discrimination, although the aspect ratio itself was less readily available in these stimuli as compared to the blocks. In a follow-up study with similar stimuli, Panday et al. (2012) showed that indeed the availability of curvature and curvature changes improves human perception of such stimuli and that the edges of the rectangular blocks probably disturbed the shape perception by touch.

Influence of aftereffects on shape from touch

Touching a shape for only a few seconds influences the perceived curvature of the subsequently touched shape (Vogels et al., 1996): after touching a convex shape, a flat surface will be perceived as concave and a concave shape will be perceived as even more concave; a slightly convex shape will be perceived as flat. Although the built-up of this so-called aftereffect is quite fast (a few seconds and saturation after 10 to 15 s), the decay is quite slow: after a delay of 40 s before touching the next shape, an aftereffect can still be measured, even if participants stretch and bend their fingers during this delay (Vogels et al., 1997). Van der Horst et al. (2008a) showed that also the finger tips are sensitive to a curvature aftereffect. They also showed that this aftereffect partially transferred to other fingers, so after touching a curved surface with a finger, the curvature perceived by another finger is somewhat changed. Interestingly, if curved surfaces were explored dynamically, a full transfer to the other hand occurred (van der Horst et al., 2008b).

Uznadze (1966) let observers repeatedly grasp spheres of different sizes, but always the small one with one hand and the large one with the other hand. After a sequence of about 10 to 15 of such grasps, he presented both hands with identical spheres of intermediate size. He observed that this intermediate sphere felt small to the hand used to the large sphere and large to the other hand. Kappers and Bergmann Tiest (2013) repeated and confirmed this experiment in a more quantitative way. In a subsequent study (Kappers and Bergmann Tiest, Submitted), they varied the shape of the objects and showed that this size aftereffect is at least partly a shape aftereffect: only after testing with an object of similar shape (either a sphere or a tetrahedron), there occurs a large aftereffect.

Influence of blindness on shape from touch

Norman and Bartholomew (2011) used the plastic bell pepper stimuli also in a study comparing discrimination performance of congenitally, early and late blind observers and blindfolded sighted observers. As the early and late blind observers performed better than the blindfolded sighted observers, they suggested that early visual experience plays a role in haptic shape perception. Withagen et al. (2012) performed a haptic matching experiment in which participants had to find the best match to the standard from a set of three test items. They found that blind and blindfolded sighted participants were equally accurate. However, the response times were much higher for the blindfolded sighted (adult) observers as compared to the blind observers if they had to match the exact shape of the stimuli.

Hunter (1954) measured how well blind and sighted participants could classify straight, concave and convex shapes. He found that both groups of participants had the tendency to judge a convex shape as straight, but this was more pronounced in the sighted group. Davidson (1972) also compared the performance of blind and blindfolded sighted participants in distinguishing whether a curved shape was convex, straight or concave. In his first experiment, he found that the blind performed better than the sighted. However, he also noticed that the blind used different strategies than the sighted. In his second experiment, he instructed the blindfolded sighted participants to use the strategies of the blind and then their performance improved.

Influence of age on shape from touch

Norman et al. (2013) showed that depending on the exact task, shape discrimination might or might not depend on age. In a curvature discrimination task, participants were required to explore the stimuli by using either static touch or dynamic touch. The “young” participant group consisted of individuals aged between 20 and 29 years, the “old” group participants were between 66 and 85 years. As long as the participants were allowed to use dynamic touch, there was no difference in discrimination performance between the two age groups. However, when using static touch, performance of the old group was significantly worse than that of the young group. This suggests that the cutaneous system is more sensitive to degradation with age than the kinesthetic system. Withagen et al. (2012) showed that in a haptic shape matching task, adults performed significantly better than children (mean age 9.3 years). However, sighted adults were much slower than sighted and blind children, indicating a possible speed-accuracy trade-off; blind adults were as fast as both groups of children.

Influence of shape on size perception

The shape of an object might influence its perceived size. In vision, there exists the well- known elongation bias: of two cylindrical objects with the same volume (i.e. size), the higher one is perceived as being the larger (e.g., Piaget, 1968). Krishna (2006) investigated whether a similar bias could also be observed in touch and in bimodal conditions (both vision and touch). She found that as long as vision was present (either vision alone or in combination with touch) indeed this elongation bias was found. However, if only touch was used to judge the size of the cylinders, the bias reversed: the wider of the two objects of a pair was perceived as being the larger. She suggested that in grasping a glass without looking, the diameter and thus the width of the glass is a much more salient feature than the height of the glass. In contrast, when looking at a glass, the height is more prominent.

Figure 4: Some examples of tetrahedra, spheres and cubes as used in the experiment by Kahrimanovic et al. (2010).

Kahrimanovic et al. (2010) compared the perceived sizes of spheres, cubes and tetrahedra (see Figure 4), both in a condition with weight information present, and one without. They found very substantial differences: if no weight information was available, a sphere had on average to be 60% larger in volume than a tetrahedron to be perceived as equal in size. When weight information was added (without explicitly telling participants that they could as well base their judgement on weight), the difference became somewhat smaller, but they were still around 30%. Also the perceived differences between the sizes of spheres and cubes, and those between cubes and tetrahedra were quite large. With a theoretical analysis and a second experiment, they could show that participants do not actually compare volumes, but instead use the surface area of the objects (note that spheres, cubes and tetrahedra with the same volume have different surface areas).

Two-dimensional shape from touch

Figure 5: Drawings of a stimulus after blindfolded exploring. In A examples that were already haptically recognized; in B examples that were recognized after drawing.

Recognizing two-dimensional common objects, usually in the form of raised line drawings, by just using touch is quite poor as compared to recognizing them by sight or as compared to recognizing the three-dimensional objects by touch (e.g., Ikeda and Uchikawa, 1978; Klatzky et al., 1993). Whereas in vision such drawings might be recognized almost instantaneously, in touch it may require minutes! In such tasks, it helps if categorical information about the object is given (e.g., Heller et al., 1996; Heller, 2002). Also guidance of the exploring finger helps in identifying the depicted object (Magee and Kennedy, 1980). Kennedy (1993) showed that also congenitally blind individuals who had never been exposed to such drawings before, were able to make use of them. Wijntjes et al. (2008b) showed that blindfolded sighted observers who did not recognize a certain raised line drawing, were often able to draw what they felt and then recognize their drawing visually. This shows that apparently it is very hard to integrate the serially acquired information about the line drawing into a percept of an object (See Figure 5).

An overview of studies investigating the ease or difficulty of recognizing raised line drawings by touch is given by Picard and Lebaz (2012). More details about picture recognition performance of blind individuals can be found in Heller and Ballesteros (2012).